lecture9 ee689 noise sources

8/10/2019 Lecture9 Ee689 Noise Sources

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Sam Palermo

Analog & Mixed-Signal Center

Texas A&M University

ECEN689: Special Topics in High-Speed

Links Circuits and SystemsSpring 2012

Lecture 9: Noise Sources


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Agenda

Noise source overview

Common noise sources

Noise budgeting References

Dally Ch 6

Stateye paper posted on website

2


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Noise in High-Speed Link Systems

Multiple noise sources can degrade linktiming and amplitude margin

3

[Dally]


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Noise Source Overview

Common noise sources Power supply noise

Receiver offset

Crosstalk

Inter-symbol interference

Random noise

Power supply noise

Switching current throughfinite supply impedance

causes supply voltage dropsthat vary with time andphysical location

Receiver offset

Caused by random device

mismatches4

Crosstalk One signal (aggressor)

interfering with anothersignal (victim)

On-chip coupling (capacitive)

Off-chip coupling (t-line) Near-end

Far-end


Signal dispersion causessignal to interfere with itself

Random noise

Thermal & shot noise

Clock jitter components


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Bounded and Statistical Noise Sources

Bounded or deterministicnoise sources

Have theoreticallypredictable values withdefined worst-case bounds

Allows for simple (butpessimistic) worst-caseanalysis

Examples

Crosstalk to small channel

count ISI

Receiver offset

5

Statistical or randomnoisesources

Treat noise as a random process

Source may be psuedo-random

Often characterized w/ Gaussian stats

RMS value

Probability density function (PDF)

Examples

Thermal noise

Clock jitter components

Crosstalk to large channel count

Understanding whether noise source is bounded or

random is critical to accurate link performance estimation


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Proportional and Independent Noise Sources

Some noise is proportionalto signal swing

Crosstalk

Simultaneous switchingpower supply noise

ISI

Cant overpower this noise

Larger signal = more noise

6

Some noise is independentto signal swing

RX offset

Non-IO power supply noise

Can overpower this noise

NISNN VVKV +=Total noise

Proportional noiseconstant

Signal swing

Independent noise


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Common Noise Sources

Power supply noise

Receiver offset

Crosstalk Inter-symbol interference

Random noise

7


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Power Supply Noise

Circuits draw current from the VDD supply nets andreturn current to the GND nets

Supply networks have finite impedance Time-varying (switching) currents induce variations on

the supply voltage

Supply noise a circuit sees depends on its location in

supply distribution network 8

[Hodges]


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Power Routing

9

Bad Block B will

experience excessivesupply noise

Better Block B will experience 1/2

supply noise, but at the cost of doublethe power routing through blocks

Even Better Block A &B will experience similarsupply noise

Best Block A & Bare more isolated

[Hodges]

[Hodges]


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Supply Induced Delay Variation

Supply noise can induce variations in circuit delay Results in deterministic jitter on clocks & data signals

10

( ) ( )

( ) ( )

VDDVVDD

VDD

VVDDCvW

VDDC

LEVVDD

VVDDCvW

VDDC

I

VDDCt

TN

TNoxsatN

L

NCNTN

TNoxsatN

L

DSATN

LPHL

+

==

Delay

2

222

CMOS delay is approximately directly proportional to VDD

More delay results in more deterministic jitter

[Hodges]


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Simultaneous Switching Noise

Finite supply impedancecauses significantSimultaneous SwitchingOutput (SSO) noise

(xtalk) SSO noise is proportional

to number of outputsswitching, n, andinversely proportional tosignal transition time, tr

11r

s

r

NtZ

LVn

t

iLV

0

==


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Power supply noise

Receiver offset


Random noise

12


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Receiver Input Referred Offset

The input referred offset is primarily a function of Vthmismatch and a weaker function of (mobility) mismatch

13WL

A

WL

At

t

V

V

== /,


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Receiver Input Referred Offset

14

WLA

WLA t

t

V

V

== /,

To reduce input offset 2x, we need to increase area 4x

Not practical due to excessive area and power consumption

Offset correction necessary to efficiently achieve good sensitivity

Ideally the offset A coefficients are given by the designkit and Monte Carlo is performed to extract offset sigma

If not, here are some common values:

AVt= 1mVm per nm of tox For our default 90nm technology, tox=2.8nm AVt~2.8mVm

Ais generally near 2%m


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Power supply noise

Receiver offset


Random noise

15


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Crosstalk

Crosstalk is noise induced by one signal (aggressor) thatinterferes with another signal (victim)

Main crosstalk sources

Coupling between on-chip (capacitive) wires Coupling between off-chip (t-line/channel) wires

Signal return coupling

Crosstalk is a proportional noise source

Cannot be reduced by scaling signal levels

Addressed by using proper signal conventions, improving channeland supply network, and using good circuit design and layouttechniques

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Crosstalk to Capacitive Lines

On-chip wires have significant capacitance to adjacentwires both on same metal layer and adjacent vertical layers

Floating victim

Examples: Sample-nodes, domino logic

When aggressor switches Signal gets coupled to victim via a capacitive voltage divider

Signal is not restored

17

OC

C

c

AcB

CC

Ck

VkV

+=

=

[Dally]


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Crosstalk to Driven Capacitive Lines

Crosstalk to a drivenline will decay awaywith a time-constant

18

( )OCOxc CCR +=

Peak crosstalk isinversely proportional

to aggressor transitiontimes, tr, and driverstrength (1/RO)

( )

( )


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Mitigating Capacitive (On-Chip) Crosstalk

Adjacent vertical metal layers should be routedperpendicular (Manhattan routing)

Limit maximum parallel routing distance

Avoid floating signals and use keeper transistors with

dynamic logic Maximize signal transition time

Trade-off with jitter sensitivity

For differential signals, periodically twist routing to make

cross-talk common-mode Separate sensitive signals

Use shield wires

Couple DC signals to appropriate supply

20


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Transmission Line Crosstalk

21

2 coupled lines:

( ) ( )dt

txdVk

dt

txdV Acx

B ,, =

Transient voltage signal on A is coupled to B capacitively

whereCS

Ccx

CC

Ck

+=

Capacitive coupling sends half the coupled energy in each direction withequal polarity

IA

IB [Dally]


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Transmission Line Crosstalk

22

2 coupled lines:

Transient current signal on A is coupled to B through mutual inductance

( ) ( )

( ) ( ) ( ) ( )dx

txdV

kdx

txdV

L

M

dt

txdI

Mdx

txdV

xL

txV

t

txI

A

lx

AAB

AA

,,,,

,,

=

==

=

where L

M

klx =

IA

IB [Dally]

Inductive coupling sends half the coupled energy in each directionwith a negative forward traveling wave and a positive reversetraveling wave


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Near- and Far-End Crosstalk

23

[Dally] ( )

( )

2

4

lxcxfx

lxcxrx

kkk

kkk

=

+=

For derivation ofkrxand kfx, seeDally 6.3.2.3

Reverse Coupling Coefficient

krx(NEXT)

Forward Coupling Coefficient

kfx(FEXT)tx


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24

Off-Chip Crosstalk

Occurs mostly inpackage and board-to-board connectors

FEXT is attenuatedby channel responseand has band-passcharacteristic

NEXT directly couplesinto victim and hashigh-pass

characteristic


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Signal Return Crosstalk

Shared return path with finite impedance Return currents induce crosstalk occurs among signals

25

VkZ

ZVV xr

Rxr ==

0

:VoltageCrosstalkReturn

V

-Vxr

[Dally]


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Power supply noise

Receiver offset


Random noise

26


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Inter-Symbol Interference (ISI)

27

( )

( ) ( )

( ) ( )thtcty kk dd

=

y(1)(t) sampled relative to pulse peak:

[ 0.003 0.036 0.540 0.165 0.065 0.033 0.020 0.012 0.009 ]

k =[ -2 1 0 1 2 3 4 5 6 ]

By Linearity: y(0)(t) =-1*y(1)(t)

cursor

post-cursor ISI

pre-cursorISI

Previous bits residual state candistort the current bit, resulting ininter-symbol interference (ISI)


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Peak Distortion Analysis Example

28

( )

( )

( ) ( )

( )( )( )

( ) ( ) 288.0389.0007.0540.02

389.0

007.0

540.0

0

0

1

0

0

1

)1(

0

==

=

=

=

= >

=


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Worst-Case Eye vs Random Data Eye

Worst-case data pattern can occur at very low probability!

Considering worst-case is too pessimistic

Worst-Case Eye

100 Random Bits1000 Random Bits1e4 Random Bits

29

Constructing ISI Probability Density


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Constructing ISI Probability DensityFunction (PDF)

Using ISI probability densityfunction will yield a more accurateBER performance estimate

In order to construct the total ISIPDF, need to convolve all of the

individual ISI term PDFs together 50% probability of 1 symbol ISI and

-1 symbol ISI

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Convolving Individual ISI PDFs Together

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* =

* =

Keep going until all individual PDFs convolved together


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Complete ISI PDF

32


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Cursor PDF Data 1

33

* =

Data 1 PDF is centered about the cursor value

and varies from a maximum positive value tothe worst-case value predicted by PDA

This worst-case value occurs at a low probability!


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Cursor Cumulative Distribution Function (CDF)

For a given offset, whatis the probability of aData 1 error?

Data 1 error probabilityfor a given offset is equalto the Data 1 CDF

34

( ) ( )

=

X

dxPDFXBER


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Combining Cursor CDFs

35


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Bit-Error-Rate (BER) Distribution Eye

36

Statistical BER analysistools use this techniqueto account for ISIdistribution and also

other noise sources Example from Stateye

Note: Different channel &data rate from previousslides


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Power supply noise Receiver offset

Crosstalk


Random noise

37


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Random Noise

Random noise is unbounded and modeledstatistically

Example: Circuit thermal and shot noise

Modeled as a continuous random variabledescribed by

Probability density function (PDF)

Mean, Standard deviation,

38

( ) ( ) ( ) ( )dxxPxdxxxPxPPDF nnnnnn

=== 22 ,,


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Gaussian Distribution

Gaussian distribution is normally assumed for random noise Larger sigma value results in increased distribution spread

39

( )( )

2

2

2

2

1

nx

n exP

=


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Signal with Added Gaussian Noise

Finite probability of noise pushing signalpast threshold to yield an error

40


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Cumulative Distribution Function (CDF)

The CDF tells whatis the probabilitythat the noisesignal is less thanor equal toacertain value

41

( ) ( )( )

dueduuPx

x

u

ux

u

nn

n

=

=

== 2

2

2

2

1

[Dally]


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Error and Complimentary Error Functions

Error Function:

Relationship between normalCDF and Error Function:

The complementary errorfunction gives the probability

that the noise will exceed agiven value

42

( ) ( )= =x

uduuxerf

0

2

exp

2

( )

+=

21

2

1 xerfx

( ) ( )

=

==

221

21

2

11

xerfc

xerfxxQ

( )

==

22

1

xerfcxQ


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Bit Error Rate (BER)

43

Using erfc to predict BER:

Need a symbol of about 7for BER=10-12

Peak-to-peak value will be 2x this

[Dally]

Normal (0,1) PDF


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Noise Source Classifications

Determining whether noise source is Proportional vs Independent

Bounded vs Statistical

is important in noise budgeting

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Noise Budget Example

45

Parameter Kn RMSValue

(BER=10-12)

Peak DifferentialSwing

0.4V

RX Offset +Sensitivity

5mV

Power SupplyNoise

5mV

Residual ISI 0.05 20mV

Crosstalk 0.05 20mV

Random Noise 1mV 14mV

Attenuation 10dB = 0.684 0.274V

Total Noise 0.338V

Differential EyeHeight Margin 62mV

Peak TX differential swing of 400mVppdequalized down 10dB

200mV 63mV

+63mV

-63mV31mV

31mV

Conservative analysis Assumes all distributionscombine at worst-case

Better technique is to usestatistical BER link simulators


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Next Time

Timing Noise BER Analysis Techniques

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